Weiyang Qin

Nonlinear responses of a rub-impact overhung rotor

Abstract For a rotor system with bearings and step-diameter shaft in the oxygen pump of an engine, the contact between the rotor and the case is considered, and the chaotic response and bifurcation are investigated. The system is divided into elements of elastic support, shaft and disk, and based on the transfer matrix method, the motion equation of the system is derived, and solved by Newmark integration method. It is found that hardening the support can delay the occurrence of chaos. When rubbing begins, the grazing bifurcation will cause periodic motion to become quasi-period. With variation of system parameters, such as rotating speed, imbalance and external damping, chaotic response can be observed, along with other complex dynamics such as period- doubling bifurcation and torus bifurcation in the response.

Grazing Bifurcation in the Response of Cracked Jeffcott Rotor

A cracked rotor is modeled by a piecewise linear system due to thebreath of crack in a rotating shaft. The differential equations ofmotion for the nonsmooth system are derived and solved with thenumerical integration method. From the simulation results, it isobserved that a grazing bifurcation exists in the response. Thegrazing bifurcation can give rise to jumps between periodic motions,quasi-periodic motions from the periodic ones, chaos, and intermittentchaos.

Investigation of snap-through and homoclinic bifurcation of a magnet-induced buckled energy harvester by the Melnikov method.

Snap-through is used to improve the efficiencies of energy harvesters and extend their effective frequency bandwidths. This work uses the Melnikov method to explore the underlying snap-through mechanism and the conditions necessary for homoclinic bifurcations in a magnet-induced buckled energy harvester. First, an electromechanical model of the energy harvester is established analytically using the Euler-Bernoulli beam theory and the extended Hamiltons principle. Second, the Melnikov function of the model is derived, and the necessary conditions for homoclinic bifurcations and chaos are presented on the basis of this model. The analysis reveals that the distance between the magnets and the end-block mass significantly affect the thresholds for chaotic motions and the high-energy solutions. Numerical and experimental studies confirm these analytical predictions and provide guidelines for optimum design of the magnet-induced buckled energy harvester.